Why can't you reheat pasta in a microwave, grill, or wok?

If you're going to reheat pasta, microwaving is a good way. Adding a few drops of water and covering helps the texture if it doesn't have sauce already on it.

You can actually do something close to a stir fry - heat some oil and use it to cook tasty ingredients (onions, garlic, herbs, spices) and then stir in the pasta (and things like olives or sweetcorn that might want heating but don't need cooking) over a gentle heat until hot enough to serve.

Grilling is less good, but still not impossible for some dishes. For bare pasta it will dry out it, but immerse in sauce and top with cheese and you can get something nice. Strictly speaking the grill doesn't do the reheating, the (hot) sauce does - a grill would burn the top before the bottom is hot.

Uncooked pasta (fresh, partly dried or fully dried) needs to be boiled in water because it needs to absorb water in order to become soft.

Pasta which has already been fully cooked, ready to eat, and then cooled down (i.e. leftovers) already contains enough water. So it can be reheated in any way you like. However, microwaving pasta leftovers without a sauce or with a "fat only" sauce (such as spaghetti aglio e olio, with just garlic and olive oil) will result in a somewhat peculiar texture. So either microwave together with a "watery" sauce, or stir-fry (or find out that you like it that way). With grilling you need to be careful not to dry the pasta out too much.

There is a third variety: Asian-style noodles are often sold in pre-cooked and then dried form. Since they are dried, they also need to absorb water. You typically soak them in hot but not boiling water. I have never seen European-style pasta in that form, but still included this for completeness.